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Thank you Michele, I will give it a read! :)

thanks!! :) @Astrophysics

is this some sort of new language??? lol

no, the quaternions were introduced by W. R. Hamilton in the far 1833 :) lol

lol looks very complicated

no, they are not complicated, please study my definitions first @oleg3321

Very easy to understand, thanks again!

Thanks! @welshfella

I remember my calc 3 teacher mentioning those to look at if you got bored..
thanks @Michele_Laino

thanks! :) @DanJS

Thank you @Michele_Laino .
I will definitely give it a read

Thanks! :) @arindameducationusc

quaternions aren't a field, they are a division ring

Quaternions are a field @oldrin.bataku

I wrote that formula:
\[{\mathbf{ij}} = - {\mathbf{ji}} = {\mathbf{k}}\]

I never worked with non-commutative algebra

I meant I never cited non-commutative algebra

:) right

field is not commonly used in mathematics literature for a skew field, this isn't the 1800s anymore